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Search: id:A154996
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| A154996 |
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a(n)=5*a(n-1)+20*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=9 . |
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+0
3
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| 1, 1, 9, 65, 505, 3825, 29225, 222625, 1697625, 12940625, 98655625, 752090625, 5733565625, 43709640625, 333219515625, 2540290390625, 19365842265625, 147635019140625, 1125491941015625, 8580160087890625, 65410639259765625
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: (1-4*x-16*x^2)/(1-5*x-20*x^2) . a(n+1)=Sum_{k, 0<=k<=n}A154929(n,k)*4^(n-k).
a(n)=(1/2)*{[(5/2)-(1/2)*sqrt(105)]^(n-1)+[(5/2)+(1/2)*sqrt(105)]^(n-1)}+(13/210)*sqrt(105)*{[(5/2)+(1/2)*sqrt(105)]^(n-1)-[(5/2)-(1/2)*sqrt(105)]^(n-1)}+(4/5)*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Jan 20 2009]
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CROSSREFS
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Adjacent sequences: A154993 A154994 A154995 this_sequence A154997 A154998 A154999
Sequence in context: A037548 A036731 A020234 this_sequence A128195 A103459 A100311
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 18 2009
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